A Semiparametric Bayesian Model for Circular-Linear Regression

Circular data are observations that are represented as points on a unit circle. Times of day and directions of wind are two such examples. In this work, we present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is useful especially when the likelihood surface is ill behaved. Markov chain Monte Carlo techniques are used to fit the proposed model and to generate predictions. The method is illustrated using an environmental data set.